Choose by schedule convenience and not carrier. Each of those 4 has advantages and disadvantages but presuming no initial status AA lets you earn status the fastest (via Gold/Platinum challenge) and that becomes a significant benefit (able to use F check-in, for example, and the prefered security line at some US airports). AA does require 4 flights on AA for status (not clear if it is enforced, but likely to be) so that might be a consideration. Combined with the 34 inch pitch on AA this does give AA the edge if your daughter isn't already QF Gold or better.